Centripetal Acceleration

1. Jul 16, 2007

rash219

Centripetal Acceleration !!!

1. The problem statement, all variables and given/known data

An Engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. He does so by banking the road in such a way that the force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the path
a. Show that for a given speed v and radius r the curve must be banked at an angle $$\Theta$$ such that tan$$\Theta$$ = v^2/r * g

2. Relevant equations

a_c (centripetal acceleration) = V^2 / r
$$\Sigma$$F_y = m * a = 0

3. The attempt at a solution

i hope this diag. makes sense to you.....

According to the question a_c = n * Sin$$\Theta$$ ---- (1)

Then

$$\Sigma$$F_y = m * a = 0
(n * Cos $$\Theta$$) - (m * g) = 0
n = (m * g) / (Cos $$\Theta$$) -------- (2)

substitute 2 in 1 for n

a_c = (m * g) / (Cos $$\Theta$$) * Sin$$\Theta$$
= (m * g) Tan $$\Theta$$

now a_c (centripetal acceleration) = V^2 / r

therefore (V^2 / r) = (m * g) Tan $$\Theta$$

and Tan $$\Theta$$ = (V^2) /(m * g * r)

what am i doing wrong ?.?

2. Jul 16, 2007

PhanthomJay

Check your equation (1) again, you have identified the centripetal force, not the centripetal acceleration.

3. Jul 16, 2007

rash219

Thanks!!! worked out right...